Minimum value of f(x)=(x^p)/(p)+(x^(-q))/(q) subjected to 1/p+1/q=1 and p>1 Although I have solved it using derivative. But did not understand how can i solve without derivative, Help Required, Thanks

maredilunavy

maredilunavy

Answered question

2022-09-14

minimum value of f ( x ) without the use of derivative
Although I have solved it using derivative. But did not understand how can i solve
without derivative, Help Required, Thanks

Answer & Explanation

altaryjny94

altaryjny94

Beginner2022-09-15Added 14 answers

Use Young's inequality.
f ( x ) = x p p + x q q x 1 x = 1.
Since f ( 1 ) = 1, the minimum is 1
Krish Crosby

Krish Crosby

Beginner2022-09-16Added 3 answers

By AM-GM:
x p p + x q q 1 p + 1 q + x + 1 x 2 1 p + 1 q = 1
Since x p p x + p 1 0 and x q q x + q 1 0

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